Statistics Weekly 2: Finding Measures of Center on
Statistics Weekly 2: Finding Measures of Center on the Calculator
Name:___________________
First a little review…
Review of Stats Weekly 11) What are the three measures of center?
2) What is an outlier?
3) Which measure of center is resistant to outliers?
Review of Section 1.5Enter the following data lists into your calculator:
The reported length of the 2008 KML Statistics students’ feet in centimeters:
L1: { 23, 33, 27, 25, 24, 29, 25, 23, 27, 25, 31, 29, 31, 29, 31, 26, 30}
Number of “hits” to the stats class website by 40 students at Cal Poly:
L2: {20, 37, 4, 20, 0, 84, 14, 36, 5, 331, 19, 0, 0, 22, 3, 13, 14, 36, 4, 0, 18, 8, 0, 26, 4, 0, 5, 23, 19, 7, 12,
8, 13, 16, 21, 7, 13, 12, 8, 42}
The percent of copper content in Bidri art from India in England’s Victoria and Albert Museum:
L3: {2.0, 2.4, 2.5, 2.6, 2.6, 2.7, 2.7, 2.8, 3.0, 3.1, 3.2, 3.3, 3.3, 3.4, 3.4, 3.6, 3.6, 3.6, 3.6, 3.7, 4.4, 4.6, 4.7,
4.8, 5.3, 10.1}
(Remember to double-check that you typed the data in correctly!!)
Now for the new stuff….
Finding the mean, median, and midrange (and other statistics) of large data sets is very time consuming.
Because computers and calculators can process data very quickly, these computing devices have
revolutionized the data analysis world!
There are a few ways you can use the statistical features of your calculator to find these measures of
center.
1) Using the LIST menu:
1) You should already have the
data you want to work with in a
list on your calculator. We’ll use
the data you entered in the
review.
2) To perform operations on lists
of data on the calculator, hit 2nd
and STAT to enter the LIST
menu.
3) The LIST “NAMES” menu
allows you to call up any list
stored on your calculator. This
includes lists L1 through L6 as
well as those you’ve created on
your own.
4) The LIST “OPS” menu has a
number of list operations you can
perform, but we will not use
these for now.
5) The LIST “MATH” menu has
what we need right now.
6) min( and max( are used to find
the minimum and maximum of a
list. (Remember you can call up
L1 by pressing 2nd “1” or LIST
“NAMES”1.) Try it!
7) mean(, median(, and sum( are
used to find the mean, median, or
sum of a list. (Remember, you
can get L2 by pressing 2nd “2” or
LIST “NAMES”2.) Note: The
“sum” is Σx for the list. Try it!
8) The calculator does not have a
midrange command, but you
could type in the command above
to find the midrange of list 2! ☺
Try it!
9) You could also find the
midrange by typing in the
commands as in part 6 above,
then use the numbers to find the
midrange. Here’s the midrange
for list 1.
2) Using 1-Var Stats:
1) Finding the measures of center
one at a time is also time
consuming. To find them all at
once, use the “1-Var Stats”
command. First hit the “STAT”
button.
2) Then go over to the CALC
menu. You will use this menu
often, but the only command we
want right now is the first one –
“1-Var Stats”.
3) To have the calculator find all
of the statistics on a single list,
call up the “1-Var Stats”
command followed by the name
of the list you want the statistics
about. Here we’ll use L2.
4) Notice the calculator gives the
mean as x . It also gives Σx, and
the sample size (n). Remember
∑x
that x =
n
5) Note there is a down arrow on
the screen. If you hit the down
arrow on you calculator, you will
scroll the screen down to show
the rest of the 1-Var Stats…
6) Scrolling down gives you the
min, max, and median for the
data list. You can find the
midrange using the values of the
min and max. (We’ll use Q1 and
Q3 in a future statistics weekly.)
Homework:
Use your calculator to find the mean, median, and midrange of the following data. Use the correct
mathematical symbols with your answers as you did in the first Statistics weekly. Put the data into the
lists indicated (keep the practice data in L1-L3 too):
1) The time in seconds for oil rig workers to escape during fire drill practice:
L4: {389, 356, 359, 363, 375, 424, 325, 394, 402, 373, 373, 370, 364, 366, 364, 325, 339, 393, 392, 369,
374, 359, 356, 403, 334, 397}
2) The percentage of juice lost after thawing frozen strawberries:
L5: {46, 51, 44, 50, 33, 46, 60, 41, 55, 46, 53, 53, 42, 44, 50, 54, 46, 41, 48}
3) The cadence (strides per second) of 20 healthy men:
L6: {.95, .85, .92, .95, .93, .86, 1.00, .92, .85, .81, .78, .93, .93, 1.05, .93, 1.06, 1.06, .96 .81, .96}
4) Give the Σx for each of the lists of data from problems1-3 (lists 4-6).
5) In the examples, the mean, median, and midrange for L2 was given on the calculator screen. Rewrite
each of those values below. Which of these measures of center should be the one reported as the average
number of “hits” to the website? Why?
Other cool stuff your calculator can do:
2) Once you use “1-Var Stats” for
a list, all of the statistics that are
calculated for a list are stored in
the calculator’s memory (until 1Var Stats is run again). You can
call up these values from the
VARS #5:Statistics menu
1) The SortA( and SortD(
commands will sort a list for you
–either ascending or descending.
This will order your data so you
can manually find the median.
You can also view a list on the
home screen by calling up its
name and hitting enter. Use the
left and right arrows to scroll
through it.
Here you can call up “n”, x ,
min, max, and Σx. You can find
the mean by using the formula:
∑ x ! (Note: I ran 1-Var
x=
n
Stats L1 first for these results…)
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